John Henry Constantine Whitehead FRS (11 November 1904 – 8 May 1960), known as "Henry", was a British mathematician and was one of the founders of

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which Map (mathematics), maps can come with homotopy, homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipli ...

. He was born in

Chennai Chennai, also known as Madras (List of renamed places in India#Tamil Nadu, its official name until 1996), is the capital city, capital and List of cities in Tamil Nadu by population, largest city of Tamil Nadu, the southernmost states and ...

(then known as Madras), in

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

, and died in

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

, in 1960.

Life

J. H. C. (Henry) Whitehead was the son of the Right Rev. Henry Whitehead, Bishop of Madras, who had studied mathematics at

Oxford Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the List of oldest universities in continuou ...

, and was the nephew of

Alfred North Whitehead Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, inclu ...

and Isobel Duncan. He was brought up in

, went to Eton and read mathematics at

Balliol College Balliol College () is a constituent college of the University of Oxford. Founded in 1263 by nobleman John I de Balliol, it has a claim to be the oldest college in Oxford and the English-speaking world. With a governing body of a master and ar ...

. After a year working as a stockbroker, at Buckmaster & Moore, he started a PhD in 1929 at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

. His thesis, titled ''The representation of

projective space In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally ...

s'', was written under the direction of

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lo ...

in 1930. While in Princeton, he also worked with

Solomon Lefschetz Solomon Lefschetz (; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equatio ...

. He became a fellow of Balliol in 1933. In 1934 he married the concert pianist Barbara Smyth, great-great-granddaughter of Elizabeth Fry and a cousin of Peter Pears; they had two sons. In 1936, he co-founded The Invariant Society, the student mathematics society at Oxford. During the Second World War he worked on

operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...

for submarine warfare. Later, he joined the codebreakers at

Bletchley Park Bletchley Park is an English country house and Bletchley Park estate, estate in Bletchley, Milton Keynes (Buckinghamshire), that became the principal centre of Allies of World War II, Allied World War II cryptography, code-breaking during the S ...

, and by 1945 was one of some fifteen mathematicians working in the " Newmanry", a section headed by

Max Newman Maxwell Herman Alexander Newman, FRS (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...

and responsible for breaking a German

teleprinter A teleprinter (teletypewriter, teletype or TTY) is an electromechanical device that can be used to send and receive typed messages through various communications channels, in both point-to-point (telecommunications), point-to-point and point- ...

cipher using machine methods.Paul Gannon, ''Colossus: Bletchley Park's Greatest Secret'', 2006, Atlantic Books; . p. 347 Those methods included the Colossus machines, early digital electronic computers. From 1947 to 1960 he was the Waynflete Professor of Pure Mathematics at

Magdalen College, Oxford Magdalen College ( ) is a Colleges of the University of Oxford, constituent college of the University of Oxford. It was founded in 1458 by Bishop of Winchester William of Waynflete. It is one of the wealthiest Oxford colleges, as of 2022, and ...

. He became president of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

(LMS) in 1953, a post he held until 1955. The LMS established two prizes in memory of Whitehead. The first is the annually awarded, to multiple recipients, Whitehead Prize; the second a biennially awarded

Senior Whitehead Prize The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally r ...

. Joseph J. Rotman, in his book on algebraic topology, as a tribute to Whitehead's intellect, says, "There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead." Whitehead died from an asymptomatic heart attack during a visit to Princeton University in May 1960. In the late 1950s, Whitehead had approached

Robert Maxwell Ian Robert Maxwell (born Ján Ludvík Hyman Binyamin Hoch; 10 June 1923 – 5 November 1991) was a Czechoslovakia, Czechoslovak-born British media proprietor, politician and fraudster. After escaping the German occupation of Czechoslovakia, ...

, then chairman of

Pergamon Press Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The c ...

, to start a new journal, ''Topology'', however Whitehead died before its first edition appeared in 1962.

Work

Whitehead's definition of

CW complex In mathematics, and specifically in topology, a CW complex (also cellular complex or cell complex) is a topological space that is built by gluing together topological balls (so-called ''cells'') of different dimensions in specific ways. It generali ...

es gave a setting for homotopy theory that became standard. He introduced the idea of simple homotopy theory, which was later much developed in connection with

algebraic K-theory Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sens ...

. The Whitehead product is an operation in homotopy theory. The

Whitehead problem In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Saharon Shelah proved that Whitehead's problem is independent of ZFC, the standard axioms of set theory. Refinement Assume that ''A'' is an a ...

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commu ...

s was solved (as an independence proof) by

Saharon Shelah Saharon Shelah (; , ; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Biography Shelah was born in Jerusalem on July 3, 1945. He is th ...

. His involvement with topology and the

Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured b ...

led to the creation of the Whitehead manifold. The definition of

crossed module In mathematics, and especially in homotopy theory, a crossed module consists of groups G and H, where G acts on H by automorphisms (which we will write on the left, (g,h) \mapsto g \cdot h , and a homomorphism of groups : d\colon H \longrighta ...

s is due to him. He also made important contributions in

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

, particularly on triangulations and their associated

smooth structure In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows mathematical analysis to be performed on the manifold. Definition A smooth structure on a manifold M ...

s. See also: Algebraic homotopy

Selected publications

* * J. H. C. Whitehead, ''On incidence matrices, nuclei and homotopy types'', Ann. of Math. (2) 42 (1941), 1197–1239. * J. H. C. Whitehead, ''Combinatorial homotopy. I.'', Bull. Amer. Math. Soc. 55 (1949), 213–245 * J. H. C. Whitehead, ''Combinatorial homotopy. II.'', Bull. Amer. Math. Soc. 55 (1949), 453–496 * J. H. C. Whitehead, ''A certain exact sequence'', Ann. of Math. (2) 52 (1950), 51–110 * J. H. C. Whitehead, ''Simple homotopy types'', Amer. J. Math. 72 (1950), 1–57. * Saunders MacLane, J. H. C. Whitehead, ''On the 3-type of a complex'', Proc. Natl. Acad. Sci. USA 36 (1950), 41–48. * ( published posthumously)

References

External links

* * {{DEFAULTSORT:Whitehead, J. H. C 1904 births 1960 deaths 20th-century British mathematicians British topologists People educated at Eton College Alumni of Balliol College, Oxford Fellows of Magdalen College, Oxford Princeton University alumni Bletchley Park people Fellows of the Royal Society Fellows of Balliol College, Oxford Waynflete Professors of Pure Mathematics